Then, you can add a second attribute for the time in seconds where you wish for the video to start:
{{< youtube oXi76HDygi8 706 >}}
My example uses default Zurb Foundation styling to make it responsive, so you will need to style it yourself. The point is, adding the start parameter.
I found a way that works as it looks like you need to add the start time as part of the query string. I copied the original internal shortcode code for youtube.html and named it youtubetime.html. Then I used the following:
With embedded youtube the arg is start in seconds, not t like a normal url.
You can see this when you click share on youtube and click embedded and then click the “start at” checkbox.